Under the assumption that the step size \(\eta \)  is sufficiently small so that \(\psi - \eta L\)  is convex on the iterates, we can apply the convergence rate of mirror descent  [1]}:
\( L(w_t) - L(w^\star ) \le \frac{1}{\eta t} D_{\psi }\left(w^\star ,w_0\right) \) 
